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Gnesinka [82]
3 years ago
15

In the opening scene of the movie Raiders of the Lost Ark, Indiana Jones replaces a golden statue with a bag of sand. The platfo

rm on which the statue is placed is designed to detect the mass of the statue. If the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues.
The density of gold is about 20\text{ g/cm}^320 g/cm
3
20, start text, space, g, slash, c, m, end text, cubed. The density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm
3
2, point, 5, start text, space, g, slash, c, m, end text, cubed. The solid-gold statue can be modeled as a cylinder with height 15\text{ cm}15 cm15, start text, space, c, m, end text and radius 4\text{ cm}4 cm4, start text, space, c, m, end text.
In terms of \piπpi, what is the volume of sand Indiana Jones needs to avoid triggering the mechanism?
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
3 0

Answer:

1920π

Step-by-step explanation:

First, you need to find the volume of the statue in terms of pi.

Volume of cylinder formula:

V=πr²h

V=π4²15

V=π16×15

V=240π

Then, you need to find the mass of the statue.

Mass:

Mass= density × volume

Mass=20×240π

Mass=4800π

Now, you need to find the volume. Since the sand has to weigh the same as the statue, the mass is going to stay the same. To find the volume you need to do:

V=mass of sand/density

V=4800π/2.5

That gives you your answer:

1920π

Note: I had to do the exact same problem on Khan Academy. This is right.

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Step-by-step explanation:

It's half the angle at the centre

½×80 = 40

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Let us assume the larger number = x
Let us assume the smaller number = y
Then
x + y = 3 3/4
x + y = 15/4
And
x/3 = (2y/3) + 1/2
x = [3 * (2y/3)] + (3/2)
  = 2y + (3/2)
Now putting the value of x from the second equation to the first , we get
x + y = 15/4
2y + (3/2) + y = 15/4
3y = (15/4) - (3/2)
3y = (15 - 6)/4
3y * 4 = 9
12y = 9
y = 9/12
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Now putting the value of y in the first equation, we get
x + y = 15/4
x + (3/4) = (15/4)
x = (15/4) - (3/4)
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3 years ago
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Setler79 [48]
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In the year 2019, Lee County used approximately 55 million gallons of water. Historical trends show that each year the water dem
Harlamova29_29 [7]

Answer:

Approximately 62 gallons of water will be used by Lee County by the year 2025.

Step-by-step explanation:

The amount, in millions gallons of water, spent by Lee County, in t years after 2019, is given by the following equation:

P(t) = P(0)(1 + r)^{t}

In which P(0) is the amount spent on 2019 and r is the increse rate, as a decimal.

In the year 2019, Lee County used approximately 55 million gallons of water.

This means that P(0) = 55

Historical trends show that each year the water demand is increasing by a rate of approximately 2.1%.

This means that r = 0.021

So

P(t) = P(0)(1 + r)^{t}

P(t) = 55(1 + 0.021)^{t}

P(t) = 55(1.021)^{t}

Approximately how many million gallons of water will be used by Lee County by the year 2025?

2025 is 2025 - 2019 = 6 years after 2019. So this is P(6).

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P(6) = 55(1.021)^{6}

P(6) = 62.3

Rounded to the nearest millions

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